Formula looks familiar, but like the man said, it's Sunday and my eyes are half closed anyway.
However, using the VIX is definitely wrong, for the following reasons:

1 - VIX is the average of the implied volatilities for the entire set of options, not any particular one. Each option within an expiration has its own IV.
2 - The figure quoted right now is the implied volatility right at this moment for the blended IV of Sept & Oct, so it doesn't have anything to do with what you're looking at.
3 - On top of that, it's for SPX options, not SPY, and so varies slightly anyway.